A typical medicine box generally has one or more drug grids for the users to store medicine according to the dosage, thus facilitating carrying and medicine taking. In existing medicine boxes, the casing has a mouth on the top, and a cover on the mouth, with the medicine in the casing. When taking out the medicine, the box is opened entirely and the medicine is removed. Because of the large mouth, excess medicine above the prescribed dosage may be dispended from the box, and therefore need to be put back. This practice can lead to contamination of the medicine in the box.